The difficulties that primary students experience when dealing with real-world related word problems have been discussed extensively. These difficulties are not only related to complex, non-routine problems but already occur with respect to routine problems that involve the application of a simple algorithm. Due to difficulties with the…

Simultaneous renewal in teacher education is based on the notion that improvement at 1 level requires improvement at all levels and that all stakeholders are responsible for such improvement. The authors discuss the creation and impact of a mathematics team as a vehicle for simultaneous renewal by using the team model for simultaneous renewal for…

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and…

Meaningful educational activities and cognitive tools might improve students' active involvements in the teaching-learning process and encourage their reflections on the concepts and relations to be investigated. It is claimed that usage of manipulatives not only increase students' conceptual understanding and problem solving skills but also…

An interesting and effective way to showcase the wide variety of fields to which differential equations can be applied is to have students give short oral presentations on a specific application. These talks, which have been presented by 30-40 students per year in our differential equations classes, provide exposure to a diverse array of topics…

In three studies, we investigated to what extent a geometrical representation in a psychological space succeeds in predicting typicality in animal, natural food and artifact concepts and whether contrast categories contribute to the prediction. In Study 1, we compared the predictive value of a family resemblance-based prototype model with a…

Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (J. S. Roberts, 1995; W. H. Van Schuur and H. A. L. Kiers, 1994). Advances in…

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

The concept of fuzzy time series is introduced and used to forecast the enrollment of a university. Fuzzy time series, an aspect of fuzzy set theory, forecasts enrollment using a first-order time-invariant model. To evaluate the model, the conventional linear regression technique is applied and the predicted values obtained are compared to the…

The objective of this investigation was to take a small data set that represents unbalanced factorial designs and explain by example how the variance is partitioned when using the various options from the Statistical Package for the Social Sciences (SPSSX) and Statistical Analysis System (SAS). That the unequal cell size analysis of variance…

Current omnibus procedures for the analysis of interaction effects in repeated measures designs which contain a grouping variable are known to be nonrobust to violations of multisample sphericity, particularly when group sizes are unequal. An alternative approach is to formulate a comprehensive set of contrasts on the data which probe the specific…

The multitrait-multimethod (MTMM) paradigm is used widely to assess construct validity, but D. A. Kenny and D. A. Kashy (1992) lament that even after 30 years we still do not know how to analyze MTMM data. The Composite Direct Product (CDP) model has recently attracted considerable attention. Its strengths and weaknesses are evaluated, and a…

A simple scheme is proposed for smoothly approximating the ability distribution for relatively long tests, assuming that the item characteristic curves (ICCs) are known or well estimated. The scheme works for a general class of ICCs and is guaranteed to completely recover the theta distribution as the test length increases. The proposed method of…

Diagnosing cognitive errors possessed by examinees can be considered as a pattern classification problem that is designed to classify a sequential input of stimuli into one of several predetermined groups. The sequential inputs in this paper's context are item responses, and the predetermined groups are various states of knowledge resulting from…

Statistical significance is often inappropriately equated with evaluating result importance and evaluating result replicability, even though these are three somewhat different issues. The prudent researcher must separately assess each of these elements of the "research triumvirate" by using different methods. This paper focuses on two…